Question-38825

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Question Number 38825 by Sr@2004 last updated on 30/Jun/18

Commented by kunal1234523 last updated on 30/Jun/18

sir Sr@2004 you can write here very easily.

$${sir}\:{Sr}@\mathrm{2004}\:{you}\:{can}\:{write}\:{here}\:{very}\:{easily}. \\ $$

Commented by Sr@2004 last updated on 30/Jun/18

$${please}\:{solve}\:{it}. \\ $$

Commented by NECx last updated on 30/Jun/18

$${please}\:{type}\:{it}\:{instead} \\ $$

Commented by Sr@2004 last updated on 30/Jun/18

$${I}\:{can}\:{not}\:{understand} \\ $$

Answered by kunal1234523 last updated on 30/Jun/18

(x+z):(y+z)= ((x/y) + 2):((y/x) + 2) ((x + z)/(y + z)) = (((x + 2y)x)/((y + 2x)y)) (x + z)(y^2 + 2xy) = (y + z)(x^2 + 2xy) xy^2 + 2x^2 y + y^2 z + 2xyz = x^2 y + 2xy^2 + x^2 z + 2xyz x^2 y − xy^2 = x^2 z − y^2 z xy^2 − y^2 z = x^2 y − x^2 z y^2 (x − z) = x^2 (y − z) ((x−z)/(y−z)) = (x^2 /y^2 ) (x−z):(y−z) = x^2 :y^2 proved

$$\left({x}+{z}\right):\left({y}+{z}\right)=\:\left(\frac{{x}}{{y}}\:+\:\mathrm{2}\right):\left(\frac{{y}}{{x}}\:+\:\mathrm{2}\right) \\ $$$$\frac{{x}\:+\:{z}}{{y}\:+\:{z}}\:=\:\frac{\left({x}\:+\:\mathrm{2}{y}\right){x}}{\left({y}\:+\:\mathrm{2}{x}\right){y}} \\ $$$$\left({x}\:+\:{z}\right)\left({y}^{\mathrm{2}} \:+\:\mathrm{2}{xy}\right)\:=\:\left({y}\:+\:{z}\right)\left({x}^{\mathrm{2}} +\:\mathrm{2}{xy}\right) \\ $$$${xy}^{\mathrm{2}} \:+\:\mathrm{2}{x}^{\mathrm{2}} {y}\:+\:{y}^{\mathrm{2}} {z}\:+\:\mathrm{2}{xyz}\:=\:{x}^{\mathrm{2}} {y}\:+\:\mathrm{2}{xy}^{\mathrm{2}} \:+\:{x}^{\mathrm{2}} {z}\:+\:\mathrm{2}{xyz} \\ $$$${x}^{\mathrm{2}} {y}\:−\:{xy}^{\mathrm{2}} \:=\:{x}^{\mathrm{2}} {z}\:−\:{y}^{\mathrm{2}} {z} \\ $$$${xy}^{\mathrm{2}} \:−\:{y}^{\mathrm{2}} {z}\:=\:{x}^{\mathrm{2}} {y}\:−\:{x}^{\mathrm{2}} {z} \\ $$$${y}^{\mathrm{2}} \left({x}\:−\:{z}\right)\:=\:{x}^{\mathrm{2}} \left({y}\:−\:{z}\right) \\ $$$$\frac{{x}−{z}}{{y}−{z}}\:=\:\frac{{x}^{\mathrm{2}} }{{y}^{\mathrm{2}} }\: \\ $$$$\left({x}−{z}\right):\left({y}−{z}\right)\:=\:{x}^{\mathrm{2}} :{y}^{\mathrm{2}} \:{proved} \\ $$

Commented by Sr@2004 last updated on 30/Jun/18